PHL 2 Lecture

8/10/2019 PHL 2 Lecture

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Logic Class NotesI. Philosophy:

a. Etymological definition: philo/philein (to love); Sophia (wisdom) -Pythagoras

b. Real definition: the science of all things by their ultimate causes andprinciples as known by natural reason alone

II. Pre-Socratics: Where does everything come from?

a. Thales: water

b. Anaximander: indeterminate boundless

c. Anaximenes: air (just as our soul, being air, holds us together, so do breathand air encompass the whole world)

d. Pythagoras: numbers (since everything is measurable and can be numbered,then everything must have originated from numbers)

e. Heraclitus of Ephesus: fire (everything that passes through fire changes, andsince what is observable in this world is that everything changes, then itmust be that there is fire in eve rything) No one can step on the same rivertwice.

f. Parmenides of Elea: the world consists of one indivisible thing; this One ismotionless and in perfect sphere. (Change is an illusion)

g. Empedocles: earth, air, fire, water (Being is uncreated and indestructible andthat it simply is. Change and motion are made possible because objects arecomposed of many particles, which are in themselves changeless.)

h. Leucippus and Democritus of Abdera: atoms (everything was the product ofthe collision of atoms moving in space)

*Pythagoras believed that every human person is incapable of knowing thewhole truth. He believed that each of these philosophers may be correct in their

views, however, they are only capable of explaining a portion of the truth but notthe whole truth.

III. Historical Development of Philosophy

a. Ancient: cosmocentric

b. Medieval: theocentric

c. Modern: ideocentric


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d. Contemporary: anthropocentric

IV. Branches of Philosophy:

a. Logic: on correct inferential thinking and its principles

b. Epistemology: on certain and true knowledge and its principles

c. Metaphysics/Ontology: on beings in general, on the different reasons andprinciples of the reality of things

d. Rational Psychology/Philosophical Anthropology: on living beings and theprinciple of life, on the nature of the vital operations and of the vital powers,and their classification

e. Cosmology/Philosophy of Nature: on the material world, and the ultimateconstituent principles of material beings

f.

Aesthetics: on beauty and harmony, on value judgments about art and beautyin general

g. Theodicy/Special Metaphysics: on the First Cause of contingent beings and ofemergent reality

h. Ethics: on human acts and their morality

i. Social/Political Philosophy: on the socialityof man, on the nature of humansociety and its principles

V. Logic:

a. Etymological definition by Zeno the Stoic: Greek, logike: a treatise on matterspertaining to thought

b. Real definition: as the science and art which helps our mind to distinguishbetween the correct from the incorrect

c. To attain clarity in our thoughts; to examine the validity of arguments andthe processes of inference

VI. Historical Development of Logic:

a. The Nyaya Philosophy (Valid knowledge is defined as the right apprehension

of an object; the manifestation of the object as it is. Thus, knowledge, to bevalid, must correspond to reality. )

b. Theory of Correspondence: Knowledge is produced when the subject comesinto contact with the object. If the generating conditions are sound, theknowledge is valid. If they are defective, knowledge is invalid.

(Kinds of Valid Knowledge)


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i. Perception (pratyaksa): non-erroneous cognition which is producedby the intercourse of sense-organs with the objects, which is notassociated with a name and which is well-defined

(2 Stages in Perception)

1. Indeterminate (Nirvikalpa): not associated with a name;inanimate apprehension, the first sense-experience which isundifferentiated, non-relational

2. Determinate (Savikalpa): well-defined; clear perception ofsomething with its attribute; of something as differentiatedand relational

(5 Requisites for the Realization of True Knowledge)

1. The object perceived

2. External requisites

3. The sense organs which are asserted for perception

4. The mind without which the organs cannot function

5. The subject who perceives

*Kants philosophy: Percepts without concepts are blind, andconcepts without percepts are empty.

ii. Inference (Anumana): a process of reasoning by which something

unperceived is known on the basis of what is known, the character ofwhich is universally applicable

(Nyaya Syllogism in Five Members)

1. First assertion/Pratijna: The hill is on fire

2. Reason/Hetu: Because it has smoke

3. Universal concomitance or instance/Udaharana: Whatever hassmoke has fire, example kitchen fire

4. Application/Upanaya: The hill has smoke which is invariably

associated with fire

5. Conclusion/Nigamana: Therefore, the hill is on fire

iii. Comparison/Analogy (Upamana): knowledge of the relation betweenthe word and its denotation

iv. Verbal Testimony (Sabda): statement of a trustworthy person andconsists in understanding its meaning


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(2 Kinds of Testimony)

1. Vaidika Testimony: found in the Vedas, considered infalliblefor they are taken to be the words of God

2. Secular Testimony: words of human beings, this liable to error

(Criteria for a Trustworthy Person)

1. The person has no intention to deceive

2. The statement of such person is not a gross contradiction towhat is already accepted as true

3. The person has established his trustworthiness in otherdomains of life

(Sources of Invalid Knowledge)

i. Memoryii. Doubt

iii. Error

iv. Hypothetical Reasoning

c. Pre-Aristotelian Logic in Greece

i. After the concern on the problem of the origin of the universe, thephilosophers turned their attention to the possibility of acquiringknowledge and on determining the validity of their thought-experiences.

ii. Thus, the use of arguments or logic.

iii. Eleatics (Zeno of Elea); Sophists (Protagoras, Gorgias, Thrasymachus);Megarics (Euclides of Megara)

iv. Zeno as founder of Dialectics

d. Aristotelian Logic

i. Aristotle (Father of Logic) made the art of argumentation into a

system.ii. Organon: collection of Aristotles (6)treatises on reasoning

VII. Logic: Nature and Divisions

a. Material Object: items or things that the science covers in its study (ex:Arithmetic: numbers)


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i. In constructing anything, whether it is a suit, or a house, or even anargument, one must have good structure or form and good material.

ii. Formal Logic discusses the conceptual patterns or structures neededfor correct and valid inference. (concerned itself with the rules

governing the structure and the validity of argument forms orpatterns)

iii. Material Logic discusses the kind of matter, that is, the nature of theterms and premises that are used in the different kinds ofdemonstration. (concerned with the meaning and truth of the conceptand sentences, which comprise a syllogism)

iv. Formal Logic coincides with our present science on correct and validinference. Material Logic is the philosophical discussion on matters ofthought and knowledge.

*This distinction does not mean that they are two separate kinds of logic. They are, in fact,complementary.

*Internal and external consistency= Valid and sound argument

All human beings are Gods creature Juan de la Cruz is a human being

Therefore, Juan de la Cruz is Gods creature.

Because it follows a sequence, this argument is valid. (Material Logic: This argument,however, is valid only insofar as Juan de la Cruz is a human being. But if Juan de la Cruz is aname of a puppet or a dog, the argument would not be sound.)

All Filipinos are God-fearers.Jose Rizal is a Filipino.

Therefore, Apolinario Mabini is a God-fearer.

Because it has no sequence, this argument is invalid.

e. Formal Logic and Dialectics

i. Some divide our present science of logic into Formal Logic andDialectics because they define Formal Logic as treatise on matterspertaining to thought while Dialectics is the treatise on argumentationor disputation.


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1. Absolute Extension: the sum total of all subjects of actualsubjects, as well as possible subjects whose nature issignified by the term and concept

2. Functional Extension: it includes only those subjects that it

actually sets before the mind when it is used in a discourse Ex: Term : Pencil

Comprehension : A writing instrument consisting of athin stick of graphite or a similar substance enclosed ina long thin piece of wood or fixed in a metal or plasticcase

Extension : types and brands of pencil; Monggol, etc.

e. Kinds of Terms:

i. Terms according to Extension

1. Singular: an idea that can be applied to one subject only

a. Proper Noun

b. Nouns modified by adjective in the superlative degree(ex. The most valuable player, the wisest man inAthens)

c. Demonstrative pronouns (this, that, those, these)

d.

Article the e. Personal Pronouns (I, you, he, she, they, we)

2. Particular: an idea that can be applied to a part or a portion ofall the members of a class

a. Indefinite pronouns or adjectives

b. Use of numbers

c. Articles a and an

d. General propositions which are true most of the timebut not always (ex: Filipinos are hospitable)

3. Universal: an idea that can be applied to all and every memberof a class

a. Universal expressions (all, every, each, whichever,whatever, none, no one, etc.)


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b. Universal idea

c. Articles a, an or the, if the idea is universal (ex: Asnake is a dangerous creature)

ii. Terms according to Definition

1. First Intention: a concept by which we understand what a thingis according to what it is in reality, whether we think of theterm or not

2. Second Intention: a concept by which we understand not onlywhat a thing is in reality but also how it is in the mind. Thispertains to how the mind is thinking of the term in a particularsituation, independent of its essence

iii. Terms according to Comprehension

1. Concrete: an idea that expresses a nature or attribute directlyand immediately inherent in a subject usually outside the mindof the knower

2. Abstract: an idea that can indirectly be referred to itsindividual subject

iv. Terms according to Meaning

1. Absolute: terms that signify a concept of the meaning of acomplete substance endowed with its independent reality. All

definitions are absolute concepts.2. Connotative: terms that signify a concept as an accident

existing in a substance. They present a form without a subject.All modifiers are connotative concepts.

v. Terms according to Quality

1. Positive: a term that asserts the presence of some attributes(ex: healthy)

2. Negative: a term that denies the presence of some attributes

(ex: unhealthy) vi. Terms according to Manner of Meaning

1. Univocal: a term that has one and the same meaning as appliedto different extensions

2. Analogous: a term that expresses a meaning that is partlydifferent and partly the same, or meanings that are related


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a. Analogous by Proportion: when a term is used in anabsolute sense in one thing and then attributed in otherthings because of some intrinsic relation with the first.Metaphorical words are classified under this kind

Ex: Healthy attributed to medicine, body, exercise, food b. Analogous by Proportionality: (also called metaphysical

analogy) when a term is used by virtue of the kindredsimilarity of the conceptual and formal reasonsdenoted.

Ex: A beautiful song is not beautiful in exactly the same wayand sense as a beautiful girl.

3. Equivocal: when the term is outwardly or apparently the same,but expressing different meanings

a. In pronunciation only: sweet-suite

b. In writing only: bow (gesture, weapon)

c. In both pronunciation and writing: ball (dance, roundtoy)

vii. Terms according to Relation

1. Contradictory: terms that mutually exclude each other to sucha degree that there is no middle ground possible (lawyer, non-

lawyer) 2. Contrary: terms that signify their extreme relations but

belonging to the same class. They allow for a middle ground.(black and white)

3. Privative: terms in which one expresses perfection and theother, the denial of that perfection in its proper subject thatought to have that perfection (sight, blindness)

4. Correlative: terms whose meanings are mutually related toeach other in such a way that the meaning of one is inreference to the other and vice-versa (mother-daughter)

f. Supposition of Terms

i. Supposition: the precise meaning a term bears in a sentence

ii. Proper Supposition: when a term stands for something for which it ispermitted to stand for literally


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1. Material: when a word is taken simply to signify the spokenword or the written symbol (ex: To run is a verb.)

2. Formal

a. Logical: when a term refers to a thing in mentalexistence (ex: Man is a universal idea)

b. Real: when a term refers to a thing in real existence(The sun rises every morning.)

iii. Improper Supposition: when a term stands for somethingmetaphorically and from its use in speech (Augustine is a SeraphicDoctor of the Church)

g. Definition of Terms:

i. Nominal Definition: expresses what the name means, not what thething is. It circumscribes the precise meaning of a given word withoutgoing into the real nature of the word

1. Etymological Definition: a definition that gives the origin of theword (Ex: Philosophy is the love of wisdom because it camefrom the words philein which means to love a nd sophiawhich means wisdom)

2. Synonymous Definition: this gives the same connotation of theterm. This kind of definition is so exact that it replaces a termwith another term in any context without changing themeaning of the definiendum. (Ex: Tiny means small)

3. Definition by Description: this gives description to thedefiniendum in such a way that it will give a picture of the termas there is no appropriate word that will give a good realdefinition of such term (Ex: A flashlight is a handy object givingoff battery-powered light)

4. Definition by Example: the definition that gives an example of adefinition for a more concrete understanding of the term (Car-

Toyota)5. Definition by Illustration: this gives a clear picture of the

definiendum through the use of illustration

6. Ostensive Definition: indicates the meaning of the term byshowing or pointing to the object. Proper names are definedostensively. (Ex: What is a pen? That is a pen.)


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ii. Real Definition: the definition that explains the essential properties ofthe object represented by the definiendum. It is usually conceived interms of the metaphysical definition.

1. Essential Definition: a definition that is constructed by the

genus and specific differencea. Definition by Genus: that which makes a thing similar to

others

b. Definition by Specific Difference: this is that whichmakes a thing different from the others

EX: A square is a polygon with four equal sides.

*The genus of the term square is polygon. Its specificdifference from other polygons is that it has four equal

sides.2. Non-Essential Definition: this definition gives the more notable

characteristics of a thing

a. Definition by Description: this is what gives the genus adescription in view of a specific difference

i. Definition by Properties: this definition gives thenatural characteristics of a thing that followsnecessarily from the essence of the thing inquestion

(Ex: Comedy is a drama of light and amusingcharacters and typically has a happy ending)

*the genus is drama and the properties are oflight and amusing characters and typically has ahappy ending.

ii. Definition by Logical Accidents: this definitionexplains a thing by giving characteristics that arecontingently connected with it. Description bylogical accidents can be through characteristicproperties, uncharacteristic properties, or ofproperties singly or collectively found in theobjects defined.

EX: (characteristic properties) Water is H 2O.


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All philosophers are lovers of wisdom

iii. Four Forms of Categorical Proposition

1. A-Proposition:

a. This asserts that the whole subject class is included inthe predicate class.

b. Quantity: Universal/Singular, Quality: Affirmative

c. All S are P

Ex: All saints are holy people.

Every philosopher is a lover of wisdom.

2. E-Proposition

a. This asserts that the whole subject class is excluded inthe predicate class.

b. Quantity: Universal/Singular, Quality: Negative

c. All S are not P/ No S is P

Ex: All sinners are not holy people.

No sinner is a saint.

3. I-Proposition

a. This asserts that part of subject class is included in thepredicate class.

b. Quantity: Particular, Quality: Affirmative

c. Some S are P

Ex: Some philosophers are atheists.

Many Filipinos are romantic lovers.

4. O-Proposition

a. This asserts that part of subject class is excluded in thepredicate class.

b. Quantity: Particular, Quality: Negative

c. Some S are not P/ Not all S are P

Ex: Some Filipinos are not patriotic.


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Not all Senators are honest politicians.

A-proposition

Universal/Singular

Affirmative

E-proposition

Universal/Singular

Negative

I-proposition

Particular

Affirmative

O-proposition

Particular

Negative

b. The Square of Opposition

c. Rules


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i. Contradictory Opposition (CD): the opposition of a pair ofpropositions that have the same subject and predicate but havedifferent quantity and different quality (A and O propositions; E and Ipropositions)

Given Contradictory

True False

False True

Ex: If some students are studious is FALSE, then, all studentsare not studious is TRUE.

ii. Contrary Opposition (CT): the opposition of two propositions thathave the same subject and predicate, and the same universal quantity

but are different as to quality (A and E propositions)

Given Contradictory

True False

False Doubtful

Ex: If all bananas are fruits is TRUE, then, no bananas arefruits will be FALSE.

If all Filipinos are artists is FALSE, then, no Filipino is anartist is DOUBTFUL.

iii. Sub-Contrary Opposition (SC): the opposition of two propositionsthat have the same subject and predicate, and the same particularquantity but are different as to quality (I and O propositions)

Given Contradictory

True Doubtful

False TrueEx: If some students are music lovers is TRUE, then, somestudents are not music lovers will be DOUBTFUL.

If not all saints are martyrs is FALSE, then, some saints aremartyrs is TRUE.


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iv. Sub-Altern Opposition (SA): the opposition of two propositions thathave the same subject and predicate, and the same affirmative qualityor the same negative quality, but are different in terms of quantity (Aand I propositions; E and O propositions)

Given Contradictory

Universal True Particular True

Universal False Particular Doubtful

Particular True Universal Doubtful

Particular False Universal True

Ex: If all students are studious is TRUE, then, some students

are studious is also TRUE.If no politician is corrupt is FALSE, then, some politicians arenot corrupt is DOUBTFUL.

If some teachers are loving persons is TRUE, then, allteachers are loving persons is DOUBTFUL.

If some monkeys are flying animals is FALSE, then, allmonkeys are flying animals is also FALSE.


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X. EductionEduction comes from the Latin word educere which means to extract. It is theprocess of immediate inference whereby from any given proposition, wederive another proposition with the same meaning but of different quantityor quality or both quantity or quality

TYPES OF EDUCTION

a. Obversion (Obv.): the process of forming the equivalent proposition bychanging the quality and the predicate of the given proposition. The givenproposition is called obvertend , while the new proposition is called theobverse .

i. Applicable to A, E, I, and O propositions. (A->E; E->A; I->O, O->I) ii. STEPS:

1. Change the quality of the given proposition (the copula)

2. Change the predicate to its contradictory or into its immediateopposed contrary terms


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3. Retain the subject and the quantity of the given proposition.

OBVERTEND (Given) OBVERSE (New)

A: All S are P E: All S are not non-P/ No S is non-P

E: All S are not P/ No S is P A: All S are non-P

I: Some S are P O: Some S are not non-P/ Not all S are non-P

O: Some S are not P/ Not all S are P I: Some S are non-P

Or

OBVERTEND (Given) OBVERSE (New)

A: All S are non-P E: All S are not P/ No S is P

E: All S are not non-P/ No S is non-P A: All S are P

I: Some S are non-P O: Some S are not P/ Not all S are P

O: Some S are not non-P/ Not all S are non-P I: Some S are P

Ex: Because all Filipinos are Asians, therefore, no Filipino is non-Asian.

b. Conversion (Conv.): the process of forming the equivalent proposition bytransposing the subject and the predicate of the given proposition. The givenproposition is called convertend , while the new proposition is called theconverse .

i. Simple Conversion: applicable to E and I propositions. (E->E; I-> I) ii. STEPS:

1. Transpose the subject and the predicate

2. Retain the quality and the quantity of the given proposition

CONVERTEND (Given) CONVERSE (New)

E: All S are not P/ No S is P E: All P are not S/ No P is S

I: Some S are P I: Some P are S


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Ex: Since no dog is a cat, no cat is a dog.

iii. Accidental Conversion: applicable to A propositions only. (A->I) iv. STEPS:

1. Transpose the subject and the predicate

2. Change the quantity of the given universal proposition intoparticular

3. Retain the quality of the given proposition

CONVERTEND (Given) CONVERSE (New)

A: All S are P I: Some P are S

Ex: All mangoes are sweet fruits, therefore, some sweet fruits are mangoes.

c. Contraposition: this is the type of immediate inference whereby from thegiven proposition, we derive a new proposition of the same meaning throughthe use of the combination of obversion and conversion

i. Partial Contraposition (PC): a combination of obversion and

conversion; Applicable to A, E, and O propositions. (A->E; E->I; O->I) ii. STEPS:

1. Obvert the given proposition

2. Convert the obverse of the given proposition

CONTRAPONEND (Given) PARTIAL CONTRAPOSIT (New)

A: All S are P E: All S are not non-P/ No S is non-P (Obv)

E: All non-P are not S/ No non-P is S(S.Conv)

E: All S are not P/ No S is P A: All S are non-P (Obv)

I: Some non-P are S. (Acc.Conv)


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O: Some S are not P/ Not all S are P I: Some S are non-P (Obv.)

I: Some non-P are S (S.Conv.)

Ex: All Christians are theists; therefore, no atheists are Christians.

Ex: No college students are illiterate; therefore, some literate are college students.

iii. Full Contraposition: a combination of obversion and conversion andanother obversion; Applicable to A, and O propositions. (A->A; O->O)

iv. STEPS:

1. Obvert the given proposition

2. Convert the obverse of the given proposition

3. Obvert the converse of the obverse of the given proposition

CONTRAPONEND (Given) FULLL CONTRAPOSIT (New)

A: All S are P E: All S are not non-P/ No S is non-P (Obv)

E: All non-P are not S/ No non-P is S(S.Conv) (PC)

A: All non-P are non-S (Obv) (FC)

O: Some S are not P/ Not all S are P I: Some S are non-P (Obv.)I: Some non-P are S (S.Conv.) (PC)

O: Some non-P are not non-S/ Not all non-Pare non-S (Obv) (FC)

Ex: Every diagram is a visual aid; therefore, every non-visual aid is a non-diagram.

d. Inversion (Inv.): the process of getting the equivalent proposition whereinthe given proposition would undergo a series of obversions and conversions.

i. Simple Inversion (S.Inv): a process of inferring a new propositionwhereby the subject of the new particular proposition is thecontradictory of the subject of the given universal proposition;Applicable to A, and E propositions. (A->O; E->I)

ii. STEPS:


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1. Change the subject of the original proposition into itscontradictory or immediately opposed contrary terms

2. Change the universal quantity into particular

3. Change the quality of the proposition

4. Retain the original predicate

INVERTEND (Given) SIMPLE INVERSE (New)

A: All S are P O: Some non-S are not P

E: All S are not P/ No S is P I: Some non-S are P

Ex: All artists are lovers of nature; therefore, not all non-artists are lovers of nature.

iii. Complete Inversion (C.Inv.): consists of inferring a new propositionwhereby the subject and the predicate of the original proposition isthe contradictory of the subject and the predicate of the newproposition. (A->I; E->O)

iv. STEPS:

1. Change the subject and the predicate of the originalproposition into its contradictory or immediately opposed

contrary terms2. Change the universal quantity into particular

3. Retain the quality of the original proposition

INVERTEND (Given) COMPLETE INVERSE (New)

A: All S are P I: Some non-S are non-P

E: All S are not P/ No S is P O: Some non-S are not non-P/ Not all non-Sare non-P

Ex: No vegetarian is a meat-lover; therefore, not all non-vegetarians are non-meatlovers.


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References:

Aguas, A Handbook in Basic Logic.

Buenaflor, The Art of Critical Thinking: Logic for Filipino Students.

Domingo and Cabantac, Rudiments of Reasoning.

Gaarder, Sophies World.

Pinon, Fundamentals of Logic.

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PHL 2 Lecture

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